Question

Problem 4. (10 Pts) Two design alternatives (X and Y) are being considered for a new ride at the Disney Theme park. Alternative X requires a $400,000 investment and will produce net annual revenue of $ BBB every year. Alternative Y requires a $ 480,000 investment and produces 1st year revenue of $ CCC; thereafter revenue decreases by S3,000 every year. Based on a (AAA + 5)% MARR, which design alternative (X or Y) has the smallest Discounted Payback Period? (AAA-1, BBB-6148, CCC-6148) Please solve using excel

Answer 1

Discounted payback period (DPBP) is the time by when a project's cumulative discounted cash flows equal zero Alternative X Year | Cash Flow (S) | PV Factor at 15% | Discounted Cash Flow (S) | Cumulative Discounted Cash Flow (S) 4,00,000 -4,00,000 -4,00,000 1.0000 3,30,963 79,393 69,037 0.8696 79,393 0.7561 60,033 2,70,930 79,393 0.6575 52,202 2,18,728 45,393 79,393 0.5718 1,73,335 79,393 1,33,862 0.4972 39,472 79,393 0.4323 34,324 -99,539 0.3759 79,393 -69,692 29,847 25,954 -43,738 79,393 0.3269 22,568 79,393 0.2843 21,170 79,393 10 0.2472 19,625 1,545 79,393 0.2149 17,065 15,520

Alternative Y Year | Cash Flow (S) | PV Factor at 15% | Discounted Cash Flow (S) | Cumulative Discounted Cash Flow (S) -4,80,000 -4,80,000 10000 -4,80,000 49,768 0.8696 43,277 -4,36,723 46,768 35,363 0.7561 -4,01,360 3,72,582 43,768 0.6575 28,778 3,49,273 40,768 0.5718 23,309 3,30,495 37,768 0.4972 18,777 34,768 0.4323 15,031 -3,15,464 0.3759 31,768 3,03,521 11,943 28,768 0.3269 2,94,117 9,404 0.2843 7,325 25,768 2,86,792 22,768 0.2472 10 5,628 2,81,164 2,76,915 19,768 0.2149 4,249 DPBP of alternative X is between 10 and 11 years. But cumulative discounted cash flow for alternative Y is still negative in year 11, which means that DPBP of alternative Y is more than 11 years. So alternative X has 2 2 4 smaller DPBP